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Re: Defining derivatives

• To: mathgroup at smc.vnet.net
• Subject: [mg87884] Re: Defining derivatives
• From: David Bailey <dave at Remove_Thisdbailey.co.uk>
• Date: Sat, 19 Apr 2008 03:35:35 -0400 (EDT)
• References: <fu9vnl$igu$1@smc.vnet.net>

dh wrote:
> Hello All,
> 
> does anybody know how to define symbolic derivatives. E.g.:
> 
> f[x_]:=f1[x];
> 
> f'[x_]:=f2[x];
> 
> this does not work because f on the lefthand side is evaluated. To 
> 
> prevent this (do not forget to remove f before redefining it):
> 
> f[x_]:=f1[x];
> 
> HoldPattern[f'[x_]]:=f2[x];
> 
> this gives no message, but f'[x] returns f1[x] instead of f2[x].
> 
> The same thinhg happens when you change the sequence of definitions:
> 
> f'[x_]:=f2[x];
> 
> f[x_]:=f1[x];
> 
> Further, where is the information about derivatives stored?
> 
> thank's a lot, Daniel
> 
> 
> 
Daniel,

Surely if f[x] has a definition, it is not unreasonable that this 
definition is used prior to differentiation. Without the definition all 
works well:

(f^\[Prime])[x_]:=f2[x];

D[f[2x],x]

2 f2[2 x]

BTW, if you only want the definition to be used for numerical cases, you 
could always use:

f[x_?NumericQ]:=f1[x]

David Bailey
http://www.dbaileyconsultancy.co.uk